Theorems · Theorem · global analysis
StructureGroupoid.id_mem_maximalAtlas
∀ {H : Type u} [inst : TopologicalSpace H] (G : StructureGroupoid H),
OpenPartialHomeomorph.refl H ∈ StructureGroupoid.maximalAtlas H GIn the model space, the identity is in any maximal atlas.
- Defined in
- Mathlib.Geometry.Manifold.HasGroupoid
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- OpenPartialHomeomorphstatement · cited by 664
- StructureGroupoidstatement and proof · cited by 121
- OpenPartialHomeomorph.reflstatement and proof · cited by 33
- StructureGroupoid.maximalAtlasstatement · cited by 28
- StructureGroupoid.subset_maximalAtlasproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- StructureGroupoid.LocalInvariantProp.liftPropAt_of_mem_maximalAtlasproof · cited by 3
- StructureGroupoid.LocalInvariantProp.liftPropAt_symm_of_mem_maximalAtlasproof · cited by 2